Math, asked by rinkesh3, 1 year ago

prove that : ( 1 - sin2 theta ) sec2 theta =1

Answers

Answered by PalakNarang
35
(1- sin^2 theta )sec ^2 theta
=( cos ^ 2 theta ) 1/ cos ^2 theta [[sin ^theta + cos^2 theta =1. and. sec ^2 theta = 1/ cos^2 theta]]
=1
Answered by AditiHegde
32

Proof for : ( 1 - sin2 theta ) sec2 theta =1 is given as follows

To prove,

(1-sin^2\theta)sec^2\theta = 1

we know the trigonometric properties,

sin^2\theta + cos^2\theta = 1

\Rightarrow 1-sin^2\theta = cos^2\theta

Therefore, we have,

LHS:

= (1-sin^2\theta)sec^2\theta

= (cos^2\theta)sec^2\theta

we know the trigonometric ratios, given by,

cos\theta = \dfrac{1}{sec\theta}

\Rightarrow sec\theta=\dfrac{1}{cos\theta}

= (\dfrac{1}{sec^2\theta})sec^2\theta

= 1

:RHS

Hence the proof.

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